基于Lorenz系统的离散分析与FPGA实现

以现场可编程门阵列(field-programmable gate array,FPGA)和IEEE754标准为基础,设计出能产生Lorenz混沌信号的数字电路. 首先,根据Euler法、Runge-Kutta法,分别将系统方程离散化. 然后,利用Verilog HDL语言编写程序,运用Xilinx软件、Modelsim软件将程序综合、编译、检测. 最终,将生成的bit文件烧录到FPGA中,通过示波器观测系统的混沌态与非混沌态. 对比论证不同算法的实现效果,得出二阶Runge-Kutta法是实现经典混沌系统的FPGA仿真的最优离散方法,为后续混沌信号在数字化领域的进一步发展提供参考和依据.

Discrete Analysis and FPGA Implementation Based on Lorenz System

Based on the field-programmable gate array(FPGA)and IEEE754 standard,digital circuits capable of generating Lorenz chaotic signals are designed and demonstrated. Firstly,the system equations are discretized according to the Euler method and the Runge-Kutta method. Then,the program is written in Verilog HDL language,and the program is integrated,compiled and tested through Xilinx software and Modelsim software. Finally,the generated bit file is burned into FPGA to observe the chaotic and non-chaotic states of the system through an oscilloscope. By comparing and demonstrating the implementation effect of different algorithms,it is concluded that the second-order Runge-Kutta method is the optimal discrete method to realize the FPGA simulation of the classical chaotic system,providing reference and basis for the further development of the subsequent chaotic signal in the digital field.